Subgroups — Dic₃₉₅₂ #72215313

Order 15808.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₉₇₆	C₂	1	2	yes	maximal
2	Dic₉₈₈	—	2	2	no	—
3	C₁₃×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₁₃×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	Dic₄₉₄	—	4	2	no	—
6	C₈×C₁₃×C₁₉	D₄	1	1	yes	characteristic
7	Dic₃₀₄	—	13	1	no	maximal, Hall
8	C₄×C₁₃×C₁₉	D₈	1	1	yes	characteristic
9	Dic₂₄₇	—	8	2	no	—
10	Dic₂₀₈	—	19	1	no	maximal, Hall
11	Dic₁₅₂	—	13	2	no	—
12	C₁₉×C₃₂	D₁₃	1	1	yes	characteristic
13	C₂×C₁₃×C₁₉	D₁₆	1	1	yes	characteristic
14	Dic₁₀₄	—	19	2	no	—
15	C₁₃×C₃₂	D₁₉	1	1	yes	characteristic
16	Dic₇₆	—	26	2	no	—
17	C₁₆×C₁₉	C₂×D₁₃	1	1	yes	characteristic
18	C₁₃×C₁₉	Q₆₄	1	1	yes	characteristic, complemented, Hall
19	Dic₅₂	—	38	2	no	—
20	C₁₃×C₁₆	C₂×D₁₉	1	1	yes	characteristic
21	Dic₃₈	—	52	2	no	—
22	C₈×C₁₉	D₅₂	1	1	yes	characteristic
23	Dic₂₆	—	76	2	no	—
24	C₈×C₁₃	D₇₆	1	1	yes	characteristic
25	C₄×C₁₉	D₁₀₄	1	1	yes	characteristic
26	Dic₁₉	—	104	2	no	—
27	Q₆₄	—	247	1	no	Sylow
28	C₄×C₁₃	D₁₅₂	1	1	yes	characteristic
29	Dic₁₃	—	152	2	no	—
30	C₂×C₁₉	D₂₀₈	1	1	yes	characteristic
31	Q₃₂	—	247	2	no	—
32	C₃₂	D₂₄₇	1	1	yes	characteristic
33	C₂×C₁₃	D₃₀₄	1	1	yes	characteristic
34	C₁₉	Dic₂₀₈	1	1	yes	characteristic, complemented, Sylow
35	Q₁₆	—	494	2	no	—
36	C₁₆	C₂×D₂₄₇	1	1	yes	characteristic
37	C₁₃	Dic₃₀₄	1	1	yes	characteristic, complemented, Sylow
38	Q₈	—	988	2	no	—
39	C₈	D₉₈₈	1	1	yes	characteristic
40	C₄	—	1976	2	no	—
41	C₄	D₁₉₇₆	1	1	yes	characteristic
42	C₂	D₃₉₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₉₅₂
commutator, cosocle	C₁₃×C₁₆×C₁₉	C₂²
Frattini	C₁₆	C₂×D₂₄₇
Fitting	C₁₃×C₁₉×C₃₂	C₂
socle, prime radical	C₂×C₁₃×C₁₉	D₁₆
hypercenter	C₃₂	D₂₄₇
hypocenter	C₁₃×C₁₉	Q₆₄
LCS	G ▷ C₁₃×C₁₆×C₁₉ ▷ C₈×C₁₃×C₁₉ ▷ C₄×C₁₃×C₁₉ ▷ C₂×C₁₃×C₁₉ ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
18. C₁₃×C₁₉	Q₆₄	semidirect
34. C₁₉	Dic₂₀₈	semidirect
37. C₁₃	Dic₃₀₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Dic₁₉₇₆	2
C₁₃×C₁₉×C₃₂	2
Dic₃₀₄	13
Dic₂₀₈	19

Subgroups — Dic3952 #72215313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃₉₅₂ #72215313